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2020hindsight said:
(and 2 mins later he'll be a further 100m etc )
Click to expand...

then again,

4. he should have stopped at the finish line, as he continues to jump half the remining distance for ever and ever amen.

i.e. he continues past the finish, yet he stays there :confused:

Questions. / multiple choice
Does he fall into a time warp at the finish line ?
Does he fall into a black hole at the finish line
or
Does he go to heaven at the finish line ?
 
2020hindsight said:
1. Reminds me of the frog who lines up at the start of a 100m track.

In his first jump he jumps 50m,
then half the remainder, (25m),
then half the remainder, (12.5m) etc

Will he ever reach the end?
I mean, he will always have half the remaining distance to go ?

2. Suppose his forward speed is constant (say 50m / min) , so that each jump is made in half the time of the previous one.

In his first jump he jumps 50m, = 1 min
then half the remainder, (25m), = 0.5 min
then half the remainder, (12.5m) = 0.25 min. etc

Will he ever reach the end?


3. But hang on!! lol
If his speed is constant (at 50m/min) - of course he will reach the end ! ;)
and it will take 2 minutes :)

(and 2 mins later he'll be a further 100m etc )
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I learnt that from the movie/book "Contact". Can't remember the name of the paradox....

In essence, movement is impossible. :cautious:
 
spooly74 said:
.....because you must go through an infinite number of steps before reaching somewhere, it should take you an infinite amount of time....
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because the frog makes an infinite number of smaller and smaller steps (approaching zero distance)

... and he does them faster and faster ( approaches infinite rate of jumping)

....... question becomes, I guess, is the distance approaching zero faster than the rate of jumping is approaching infinity? or vice versa. ?

Questions. / multiple choice
Does he fall into a time warp at the finish line ?
Does he fall into a black hole at the finish line
or
Does he go to heaven at the finish line ?
Click to expand...

PS Does the frog turn into a little pool of hot melted green butter at the finish line?
:eek:
 
Pat said:
http://en.wikipedia.org/wiki/Zeno's_paradoxes#The_Paradoxes_of_Motion
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http://en.wikipedia.org/wiki/Zeno's_paradoxes#The_Paradoxes_of_Motion

It certainly must have been a fun question for an after dinner chat at the Aristotle's house.
(not bad considering he lived 384BC - 322BC) :2twocents

Achilles and the tortoise
“ In a race, the quickest runner can never overtake the slowest, since the pursuer must first reach the point whence the pursued started, so that the slower must always hold a lead. ”
””Aristotle, Physics VI:9, 239b15

In the paradox of Achilles and the Tortoise, Achilles is in a footrace with the tortoise. Achilles allows the tortoise a head start of 100 feet. If we suppose that each racer starts running at some constant speed (one very fast and one very slow), then after some finite time, Achilles will have run 100 feet, bringing him to the tortoise's starting point. During this time, the tortoise has run a much shorter distance, for example 10 feet. It will then take Achilles some further time to run that distance, in which time the tortoise will have advanced farther; and then more time still to reach this third point, while the tortoise moves ahead. Thus, whenever Achilles reaches somewhere the tortoise has been, he still has farther to go. Therefore, because there are an infinite number of points Achilles must reach where the tortoise has already been, he can never overtake the tortoise.
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Status of the paradoxes today

Mathematicians thought they had done away with Zeno's paradoxes with the invention of the calculus and methods of handling infinite sequences by Isaac Newton and Gottfried Wilhelm Leibniz in the 17th century .....

However, some philosophers [14] insist that the deeper metaphysical questions, as raised by Zeno's paradoxes, are not addressed by the calculus. That is, while calculus tells us where and when Achilles will overtake the Tortoise, philosophers do not see how calculus takes anything away from Zeno's reasoning that concludes that this event cannot take place in the first place. Most importantly, many philosophers do not see where, according to the calculus, Zeno's reasoning goes wrong .
Click to expand...

lol - moral of the story... it doesn't pay to follow only philosophy without a bit of mathsematics as well .. ;)
 
:rant

The frog doesn't get faster, his speed is constant (which you stated) 50m/1min = 25m/0.5min = 12.5m/0.25 min....

And if he only ever jumps half of the remaining distance, he will never quite get to the 100m line.

Also, there is an issue with accuracy, it depends on how precise we can measure the thing.

Now just to complicate things, I want to throw the Heisenberg uncertainty principle out there....explanation
which basically says, you can't measure both an object's speed and position at the same time.

However, the frog should be where you expect him to be at a certain point in time, as you know the path he will take (half the distance remaining etc.)

Of course none of this matters if I stomp on him! :eek:

:end rant


PS At absolute zero, a molecule has only zero-point energy. This is Einstein stuff, I'm not Einstein. I'm Yoda. :D
 
white_crane said:
The frog doesn't get faster, his speed is constant (which you stated) 50m/1min = 25m/0.5min = 12.5m/0.25 min....

And if he only ever jumps half of the remaining distance, he will never quite get to the 100m line.
Click to expand...

He will ...this is the apparent paradox ... as you get down to the tiny distances (dividing by 2 infinity) you also get tiny lenghts of time and as you move that tiny distance infinite times you get a real distance and a real amount of time.

The series 1/2 + 1/3 + 1/4 + 1/5 + ... adds up to infinity,
but the series 1/2 + 1/4 + 1/8 + 1/16 + ... adds up to 1, bye bye Zeno.
 
spooly74 said:
The series 1/2 + 1/3 + 1/4 + 1/5 + ... adds up to infinity,
but the series 1/2 + 1/4 + 1/8 + 1/16 + ... adds up to 1, bye bye Zeno.
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sounds good to me
divergent series vs convergent series yes?

Now which type of series do they get when the energy given out by these colliding thingos starts to build as they bounce off the wall and collide some more and... ? lol :rolleyes:
 
I was thinking the frog speed is constant, but because he's jumping half distances, the poor lil frog has to leap quicker and quicker to keep his speed up... 'super frog in a sock!'
 
Pat said:
I think there's a nice little youtube cartoon type video posted on this somewhere in this thread, or the old science/astronomy type thread...

2020 do you remember?
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pat
I think you're right about Heisenberg's uncertainty principle - then again, there's a certain amount of uncertainty when I say that. ;)

(sorry m8 they don't come any cornier than that). Will look for it "later". Someone will probably beat me to it.

Personally I find some of this stuff an unnecessary headache. I mean , lol, if a frog wants to jump his way up a sprint track at 50m / min - then let him get on with it !! If he takes more than 2 minutes, then he obviously karked on the way. No need to philosophise unduly over whether or not he gets to the other end.

- and all due respect to Aristotle, but that goes for Achilles and the Tortoise as well - obviously Achilles screams past the tortoise lol ;)

- and also for Heisenberg and his Uncertainties.

Think I wrote a poem about this once when I had nothing to do :-
https://www.aussiestockforums.com/forums/showthread.php?p=88164&highlight=relative#post88164

Hard to imagine how they would have felt, exPlaining to men (stubborn mules!),
After they’d preached of their blackholed, uncertaintized, relative, fringe-dwelling rules,
Can’t you just picture it, Einstein and Herzy, Wobbling around on barstools,
"Audience laughed ven there vasn’t a joke, - Mein Gott!! vott a kreat pack of fools!".
:cool:
 
LOL!!!
Here it is, thanks spooly...


spooly74 said:
LOL but I`m pretty sure it`s Faster than light!

Here is something else you might enjoy 2020 et all.

A little look into the strange world of Quantum Physics ...but don`t let it know you are watching ;)

Click to expand...
 
Pat, a similar one, even more weird? :confused:
only 1m 09s - worth the wtach ..

"everything is still touching - space .. (is an) illusion" ;)
Personally I can't understand a word of it lol.
Any questions, ask spooly lol


Amazing Facts of Quantum Physics
 
I love those Dr Quantum vids, i'll be watching these tonight, maybe i'll have a better understanding later this evening... :rolleyes:
 

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